Is there any way to get from Dubrovnik to Korcula early in the day (rather than waiting for the 4:30 Krilo catamaran)?
You don't say when, but G&V also runs a catamaran in July and August:
http://www.gv-line.hr/raspored.php?linija=3&lang=E
Just fyi, the bus from Dubrovnik to Korcula leaves in the afternoon also: http://libertasdubrovnik.com/wp-content/uploads/voznired.pdf
As a last resort without a car, there is a shuttle run by a company called Korkyra.